4. Lattice Multiplication

We’ve made it…we can multiply small numbers using area, we can multiply small numbers pretending to do area, and we can keep pretending as we use bigger and bigger numbers.

Now comes full-blown lattice multiplication. Here we go.

How it looks at the end:

lattice

What IS that, you may wonder. It’s a mix of area model, with some old-school place value thrown in. Let’s break it down, and start over.

lattice-setup

That looks just like the area model…except no zeroes! Ok, we can deal with that. We’ll just use place value later on. Let’s multiply like area model (but we’ll do it a little off-center).

lattice-multiply

It looks more or less like area, only with the answers in corners, and no extra zeroes. That’s basically it. Now we just need to add place values just like we used to. Only instead of straight up and down, we need to go at an angle. So…let’s add imaginary lines in red to cut each box in half.

lattice-lines

Now we just need to add inside each band…they all correspond to the same place value, and we can carry (in red) to the next line.

lattice-finalFinally, the answer is there and we can read it off: 33,813!

It’s not intuitive, but if you take a little bit from all the other methods, then you end up with lattice.

Good luck!

**note: if you multiply, and the answer to go in a box is only one digit, put a zero in the upper corner:

lattice-small